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Physics newbie here, sorry if this is super basic...

I am learning about kinematic equations and am having difficulty reconciling two of the equations. Let's say I begin driving and after 1 second have gone 10 m and that I want to find what the acceleration was.

Now, $V_f = \Delta X / \Delta T$. $V_f$, then, equals $10m/s$. We know that $V_i = 0$, so $\Delta V = 10m/s$. And since $a = \Delta V / \Delta T$ , we can plug in values to find that $a=(10m/s - 0m/s)/1s$, which comes out to $10m/s^2$.

But if I use the equation $\Delta X = V_i t + \frac{a t^2}{2}$, I get a different answer for $a$. The initial velocity was $0m/s$, which means $\Delta X = \frac{a t^2}{2}$. When I plug in values, I get $10m = \frac{a t^2}{2}$ which resolves to $20m/1s^2 = a = 20m/s^2$!

I am obviously missing something, probably fundamental and basic...thank you for your help!

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closed as off-topic by CuriousOne, Gert, Diracology, Bill N, user36790 Jul 13 '16 at 3:00

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The kinematic equations are derived from differential equations. This means that you can start with the acceleration, then move to velocity, and then position given that the necessary information is available (like initial velocity or position). I find that understanding this helps me visualize the connection between the three.

You can not rely on the simple ΔV/ΔT expression for the acceleration because this is only uses the average velocity, and the velocity is changing instantaneously due to the acceleration. This instantaneous change is what motivates us to use the kinematics which are derived from differential equations. ((Differential equations relate instantaneous rates of change between variables, thus removing the error from using averages))

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